1

### IIT-JEE 1984

The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has
A
no root
B
one root
C
two equal root
D
infinitely many roots
2

### IIT-JEE 1982

The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is
A
$$- 4 < x \le 0$$
B
$$\,0 < x < 1$$
C
$$- 100 < x < 100$$
D
$$- \infty < x < \infty$$
3

### IIT-JEE 1982

If p, q, r are any real numbers, then
A
max (p, q) < max (p, q, r )
B
min (p, q) = $${1 \over 2}\left( {p + q - \left| {p - q} \right|} \right)$$
C
max (p, q) < min (p, q, r)
D
none of these
4

### IIT-JEE 1982

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at
A
town B
B
45 km from town A
C
town A
D
45 km from town B

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NEET

Class 12